Question: Solve for $x$ and $y$ using elimination. ${-5x+2y = -32}$ ${-6x-2y = -78}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-11x = -110$ $\dfrac{-11x}{{-11}} = \dfrac{-110}{{-11}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-5x+2y = -32}\thinspace$ to find $y$ ${-5}{(10)}{ + 2y = -32}$ $-50+2y = -32$ $-50{+50} + 2y = -32{+50}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 10}$ into $\thinspace {-6x-2y = -78}\thinspace$ and get the same answer for $y$ : ${-6}{(10)}{ - 2y = -78}$ ${y = 9}$